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Simplifying 2r2 + 20 = 14r Reorder the terms: 20 + 2r2 = 14r Solving 20 + 2r2 = 14r Solving for variable 'r'. Reorder the terms: 20 + -14r + 2r2 = 14r + -14r Combine like terms: 14r + -14r = 0 20 + -14r + 2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -7r + r2) = 0 Factor a trinomial. 2((2 + -1r)(5 + -1r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5Solution
r = {2, 5}
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